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Fixed Point Sets of k -Continuous Self-Maps of m -Iterated Digital Wedges

Author

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  • Sang-Eon Han

    (Department of Mathematics Education, Institute of Pure and Applied Mathematics, Jeonbuk National University, Jeonju-City Jeonbuk 54896, Korea)

Abstract

Let C k n , l be a simple closed k -curves with l elements in Z n and W : = C k n , l ∨ ⋯ ∨ C k n , l ︷ m - times be an m -iterated digital wedges of C k n , l , and F ( C o n k ( W ) ) be an alignment of fixed point sets of W . Then, the aim of the paper is devoted to investigating various properties of F ( C o n k ( W ) ) . Furthermore, when proceeding with this work, this paper addresses several unsolved problems. To be specific, we firstly formulate an alignment of fixed point sets of C k n , l , denoted by F ( C o n k ( C k n , l ) ) , where l ( ≥ 7 ) is an odd natural number and k ≠ 2 n . Secondly, given a digital image ( X , k ) with X ♯ = n , we find a certain condition that supports n − 1 , n − 2 ∈ F ( C o n k ( X ) ) . Thirdly, after finding some features of F ( C o n k ( W ) ) , we develop a method of making F ( C o n k ( W ) ) perfect according to the (even or odd) number l of C k n , l . Finally, we prove that the perfectness of F ( C o n k ( W ) ) is equivalent to that of F ( C o n k ( C k n , l ) ) . This can play an important role in studying fixed point theory and digital curve theory. This paper only deals with k -connected digital images ( X , k ) such that X ♯ ≥ 2 .

Suggested Citation

  • Sang-Eon Han, 2020. "Fixed Point Sets of k -Continuous Self-Maps of m -Iterated Digital Wedges," Mathematics, MDPI, vol. 8(9), pages 1-26, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1617-:d:415706
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    References listed on IDEAS

    as
    1. Han, Sang-Eon, 2019. "Estimation of the complexity of a digital image from the viewpoint of fixed point theory," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 236-248.
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